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This was a great question. I had fun working on it. I’m a little sad that you already posted your solution – I wanted to have a crack at working on it and posting how far I got. I was going in a similar direction as you, and I even was using the same Grapher program on the Mac to generate my curves!

I too found that as m and n increase, we tend to get something that approximates a line. I like the cobweb plots. I don’t know why I didn’t think of them immediately, since this is precisely what they’re for!

Sorry to post the solution too quickly. I posted the solution separately so readers could read the question and the solution separately, but maybe a time lag would have been better—remove all temptation!